Derivation of De Broglie Equation
The de Broglie equation, which relates the wavelength of a particle to its momentum, can be derived as follows:
Step 1: Start with the energy-momentum relationship for a photon:
E = h/ν
p = h/λ
Step 2: According to Einstein’s mass-energy equivalence, E = mc2
Step 3: De Broglie hypothesized that particles and waves have the same traits, so he equated the energies of a photon and a particle: (E = mc2 = h/ν).
Step 4: Since real particles do not travel at the speed of light, de Broglie substituted the velocity (v) for the speed of light (c), leading to the equation (mv2 = h/ν).
Step 5: Using the relationship (v = ν/λ), where (λ) is the de Broglie wavelength, de Broglie arrived at the final expression that relates the wavelength and the particle’s speed:
λ = h/mv
λ = h/p
This shows how de Broglie related the wavelength of a particle to its momentum, providing a critical insight into the wave-particle duality of matter.
Dual Nature of Matter
Dual Nature of Matter states that a matter exhibits both Particle Nature and Wave Nature. It means that when a matter is at rest it behaves like a particle and when it is moving it behaves like wave. Different Experiments have been performed to prove this by the science community.
In this article, we will look into this theory and understand the dual nature of matter. We will also learn the experiments that proved the dual nature of matter.
Table of Content
- What is Dual Nature of Matter
- Particle Nature of Light
- Compton Scattering
- Davisson and Germer Experiement
- Wave Nature of Matters
- De-Broglie Hypothesis
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